It’s the late 1980s. All across America, families are glued to their TVs as a daring rescue attempt unfolds over many frantic hours. With innocent life imperiled, the whole world extends its hands, and its prayers.

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Dermot Mulroney as a National Guardsman and Ted Danson as an oil tycoon.

No, this is not the story of Jessica McClure, the Texas toddler famously stuck in a backyard well. If the new movie “Big Miracle’’ is to be believed, the most riveting story of the ’80s was three migrating California gray whales stranded beneath miles of ice far above the Arctic Circle.

It doesn’t matter if many of us will have a hard time recalling this “based on a true story’’ event. “Big Miracle’’ doesn’t need us to swallow its hyperbole as fact. It needs only to entertain. And that it does thoroughly, leaving us both charmed and enriched without feeling very preached at. Praise be.

Ken Kwapis, the director, whose credits include “The Sisterhood of the Traveling Pants’’ and numerous episodes of “The Office,’’ goes at “Big Miracle’’ with a combination of big- and small-screen weapons. It’s probably not fair to call this “Free Willy’’ meets “Northern Exposure,’’ but it’s pretty accurate. And it’s a compliment, really. Kwapis’s movie has that unapologetic atta-boy spirit. It’s also playful without being silly.

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Kristen Bell as a TV journalist in “Big Miracle.’’

Adapted by Jack Amiel and Michael Begler from a book (“Freeing the Whales’’) by Thomas Rose, “Big Miracle’’ puts two humans at the center of its tale. Adam (John Krasinski) is a cub TV reporter doing his time in Barrow, Alaska, where big news is the arrival of avocados at the town’s first/only Mexican restaurant. One day, while out in the field, Jack spots the trio of whales spouting through a small hole in the ice. His story is picked up by the greater media. Next thing you know, Tom Brokaw’s talking about it on the “Nightly News.’’

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Enter Rachel (Drew Barrymore), Jack’s ex-girlfriend and an impassioned Greenpeace activist, who blows in with the subtlety of a blizzard. Rachel is determined to rescue the whales - now tagged Fred, Wilma, and baby Bam Bam - and to get the job done she is willing to pressure greedy oil tycoons (Ted Danson, looking more like a Q-Tip every day), crusty National Guardsman (Dermot Mulroney), and skeptical Inupiaq whalers (led by John Pingayak). Outwardly, she’s a broad caricature - no makeup (that stuff is animal tested), severely damaged hair, a wardrobe pulled from the linty bottom of the ’80s closet (not just a cowl-neck sweater, a mustard-colored cowl-neck sweater). But what makes her more than a cartoon, besides Barrymore’s considerable powers as an actress, is that she always seems clear-eyed and in on the joke. We can laugh, rather than roll our eyes, when Rachel gets a Deep Throat-like phone tip from “a friend of the whales.’’ We can weep when she makes the case for caring so deeply about these “big but vulnerable’’ creatures.

Krasinski is Krasinski, or at least he is Jim from “The Office’’ - a lovable mensch who might covet more glamorous jobs and girls (in this case, Kristen Bell as a Barbie-doll broadcaster on the rise), but who will always land with both feet on the ground, pointed in an admirable direction.

Back to those trapped whales: A variety of forces mobilize to save them, and “Big Miracle’’ has quite a lot of fun with the politics and interests at play. There are hilarious references to Ronald Reagan and those in his presidential orbit (“Gorby, it’s Ronnie,’’ begins one phone call seeking help from a Russian ship), plus one late, unlabeled cameo that I’m still chuckling over. When a plan to drag in an icebreaking hover-barge by helicopter fails, the Alaskan locals break out their chainsaws and start carving a five-mile path of holes that will lead the whales to freedom. Bam Bam is fading fast, which parents should understand means closeups of his injuries and (spoiler alert) no Hollywood ending for this “little’’ one. The movie employs convincing animatronic whales and takes significant dramatic liberties, especially in the final act, but it’s closer to the real story than most viewers will realize until the postscripts roll.

Last fall’s endearing “Dolphin Tale’’ set a high bar for family films of this kind. (One not met by the recent “We Bought a Zoo,’’ which had more pedigree than heart or humor.) “Big Miracle’’ isn’t as genuine as “Dolphin Tale,’’ and there are many more plot points that seem to be a stretch, but this latest marine adventure is every bit as free-spirited and considerably bolder. The Inupiat boy played by newcomer Ahmaogak Sweeney, for example, is a stock character - an opportunist who sells overpriced cardboard to the journalists whose delicate feet can’t stand up to the frozen ground. The surprise is that he’s a minor character, at best, and no one’s pushing him to steal a single scene.

“Big Miracle’’ is full of such simple acts of intelligence. And that’s a minor miracle.